{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "toc": true
   },
   "source": [
    "<h1>Agenda<span class=\"tocSkip\"></span></h1>\n",
    "<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#Dirichlet-process-mixtures-for-density-estimation\" data-toc-modified-id=\"Dirichlet-process-mixtures-for-density-estimation-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>Dirichlet process mixtures for density estimation</a></span><ul class=\"toc-item\"><li><span><a href=\"#Dirichlet-processes\" data-toc-modified-id=\"Dirichlet-processes-1.1\"><span class=\"toc-item-num\">1.1&nbsp;&nbsp;</span>Dirichlet processes</a></span></li><li><span><a href=\"#Dirichlet-process-mixtures\" data-toc-modified-id=\"Dirichlet-process-mixtures-1.2\"><span class=\"toc-item-num\">1.2&nbsp;&nbsp;</span>Dirichlet process mixtures</a></span></li></ul></li></ul></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Dirichlet process mixtures for density estimation\n",
    "Author: [Austin Rochford](https://github.com/AustinRochford/)\n",
    "\n",
    "## Dirichlet processes\n",
    "\n",
    "The [Dirichlet process](https://en.wikipedia.org/wiki/Dirichlet_process) is a flexible probability distribution over the space of distributions.  Most generally, a probability distribution, $P$, on a set $\\Omega$ is a [measure](https://en.wikipedia.org/wiki/Measure_(mathematics%29) that assigns measure one to the entire space ($P(\\Omega) = 1$).  A Dirichlet process $P \\sim \\textrm{DP}(\\alpha, P_0)$ is a measure that has the property that, for every finite [disjoint](https://en.wikipedia.org/wiki/Disjoint_sets) partition $S_1, \\ldots, S_n$ of $\\Omega$,\n",
    "\n",
    "$$(P(S_1), \\ldots, P(S_n)) \\sim \\textrm{Dir}(\\alpha P_0(S_1), \\ldots, \\alpha P_0(S_n)).$$\n",
    "\n",
    "Here $P_0$ is the base probability measure on the space $\\Omega$.  The precision parameter $\\alpha > 0$ controls how close samples from the Dirichlet process are to the base measure, $P_0$.  As $\\alpha \\to \\infty$, samples from the Dirichlet process approach the base measure $P_0$.\n",
    "\n",
    "Dirichlet processes have several properties that make them quite suitable to [MCMC](https://en.wikipedia.org/wiki/Markov_chain_Monte_Carlo) simulation.\n",
    "\n",
    "1.  The posterior given [i.i.d.](https://en.wikipedia.org/wiki/Independent_and_identically_distributed_random_variables) observations $\\omega_1, \\ldots, \\omega_n$ from a Dirichlet process $P \\sim \\textrm{DP}(\\alpha, P_0)$ is also a Dirichlet process with\n",
    "\n",
    "    $$P\\ |\\ \\omega_1, \\ldots, \\omega_n \\sim \\textrm{DP}\\left(\\alpha + n, \\frac{\\alpha}{\\alpha + n} P_0 + \\frac{1}{\\alpha + n} \\sum_{i = 1}^n \\delta_{\\omega_i}\\right),$$\n",
    "    \n",
    " where $\\delta$ is the [Dirac delta measure](https://en.wikipedia.org/wiki/Dirac_delta_function)\n",
    " \n",
    " $$\\begin{align*}\n",
    "     \\delta_{\\omega}(S)\n",
    "         & = \\begin{cases}\n",
    "                 1 & \\textrm{if } \\omega \\in S \\\\\n",
    "                 0 & \\textrm{if } \\omega \\not \\in S\n",
    "             \\end{cases}\n",
    " \\end{align*}.$$\n",
    "\n",
    "2. The posterior predictive distribution of a new observation is a compromise between the base measure and the observations,\n",
    "\n",
    "    $$\\omega\\ |\\ \\omega_1, \\ldots, \\omega_n \\sim \\frac{\\alpha}{\\alpha + n} P_0 + \\frac{1}{\\alpha + n} \\sum_{i = 1}^n \\delta_{\\omega_i}.$$\n",
    "\n",
    " We see that the prior precision $\\alpha$ can naturally be interpreted as a prior sample size.  The form of this posterior predictive distribution also lends itself to Gibbs sampling.\n",
    "    \n",
    "2. Samples, $P \\sim \\textrm{DP}(\\alpha, P_0)$, from a Dirichlet process are discrete with probability one.  That is, there are elements $\\omega_1, \\omega_2, \\ldots$ in $\\Omega$ and weights $w_1, w_2, \\ldots$ with $\\sum_{i = 1}^{\\infty} w_i = 1$ such that\n",
    "\n",
    "    $$P = \\sum_{i = 1}^\\infty w_i \\delta_{\\omega_i}.$$\n",
    "\n",
    "3. The [stick-breaking process](https://en.wikipedia.org/wiki/Dirichlet_process#The_stick-breaking_process) gives an explicit construction of the weights $w_i$ and samples $\\omega_i$ above that is straightforward to sample from.  If $\\beta_1, \\beta_2, \\ldots \\sim \\textrm{Beta}(1, \\alpha)$, then $w_i = \\beta_i \\prod_{j = 1}^{n - 1} (1 - \\beta_j)$.  The relationship between this representation and stick breaking may be illustrated as follows:\n",
    "    1. Start with a stick of length one.\n",
    "    2. Break the stick into two portions, the first of proportion $w_1 = \\beta_1$ and the second of proportion $1 - w_1$.\n",
    "    3. Further break the second portion into two portions, the first of proportion $\\beta_2$ and the second of proportion $1 - \\beta_2$.  The length of the first portion of this stick is $\\beta_2 (1 - \\beta_1)$; the length of the second portion is $(1 - \\beta_1) (1 - \\beta_2)$.\n",
    "    4. Continue breaking the second portion from the previous break in this manner forever.  If $\\omega_1, \\omega_2, \\ldots \\sim P_0$, then\n",
    "\n",
    "    $$P = \\sum_{i = 1}^\\infty w_i \\delta_{\\omega_i} \\sim \\textrm{DP}(\\alpha, P_0).$$\n",
    "    \n",
    "[Suggested Further Reading]: (http://mlg.eng.cam.ac.uk/tutorials/07/ywt.pdf) and (https://www.stats.ox.ac.uk/~teh/research/npbayes/Teh2010a.pdf) for a brief introduction to other flavours of Dirichlet Processes, and their applications.\n",
    "\n",
    "We can use the stick-breaking process above to easily sample from a Dirichlet process in Python.  For this example, $\\alpha = 2$ and the base distribution is $N(0, 1)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from __future__ import division"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "import numpy as np\n",
    "import pymc3 as pm\n",
    "import scipy as sp\n",
    "import seaborn as sns\n",
    "from theano import tensor as tt\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "blue, *_ = sns.color_palette()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "SEED = 5132290 # from random.org\n",
    "\n",
    "np.random.seed(SEED)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 20\n",
    "K = 30\n",
    "\n",
    "alpha = 2.\n",
    "P0 = sp.stats.norm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We draw and plot samples from the stick-breaking process."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "beta = sp.stats.beta.rvs(1, alpha, size=(N, K))\n",
    "w = np.empty_like(beta)\n",
    "w[:, 0] = beta[:, 0]\n",
    "w[:, 1:] = beta[:, 1:] * (1 - beta[:, :-1]).cumprod(axis=1)\n",
    "\n",
    "omega = P0.rvs(size=(N, K))\n",
    "\n",
    "x_plot = np.linspace(-3, 3, 200)\n",
    "\n",
    "sample_cdfs = (w[..., np.newaxis] * np.less.outer(omega, x_plot)).sum(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "ax.plot(x_plot, sample_cdfs[0], c='gray', alpha=0.75,\n",
    "        label='DP sample CDFs');\n",
    "ax.plot(x_plot, sample_cdfs[1:].T, c='gray', alpha=0.75);\n",
    "ax.plot(x_plot, P0.cdf(x_plot), c='k', label='Base CDF');\n",
    "\n",
    "ax.set_title(r'$\\alpha = {}$'.format(alpha));\n",
    "ax.legend(loc=2);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As stated above, as $\\alpha \\to \\infty$, samples from the Dirichlet process converge to the base distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (l_ax, r_ax) = plt.subplots(ncols=2, sharex=True, sharey=True, figsize=(16, 6))\n",
    "\n",
    "K = 50\n",
    "alpha = 10.\n",
    "\n",
    "beta = sp.stats.beta.rvs(1, alpha, size=(N, K))\n",
    "w = np.empty_like(beta)\n",
    "w[:, 0] = beta[:, 0]\n",
    "w[:, 1:] = beta[:, 1:] * (1 - beta[:, :-1]).cumprod(axis=1)\n",
    "\n",
    "omega = P0.rvs(size=(N, K))\n",
    "\n",
    "sample_cdfs = (w[..., np.newaxis] * np.less.outer(omega, x_plot)).sum(axis=1)\n",
    "\n",
    "l_ax.plot(x_plot, sample_cdfs[0], c='gray', alpha=0.75,\n",
    "          label='DP sample CDFs');\n",
    "l_ax.plot(x_plot, sample_cdfs[1:].T, c='gray', alpha=0.75);\n",
    "l_ax.plot(x_plot, P0.cdf(x_plot), c='k', label='Base CDF');\n",
    "\n",
    "l_ax.set_title(r'$\\alpha = {}$'.format(alpha));\n",
    "l_ax.legend(loc=2);\n",
    "\n",
    "K = 200\n",
    "alpha = 50.\n",
    "\n",
    "beta = sp.stats.beta.rvs(1, alpha, size=(N, K))\n",
    "w = np.empty_like(beta)\n",
    "w[:, 0] = beta[:, 0]\n",
    "w[:, 1:] = beta[:, 1:] * (1 - beta[:, :-1]).cumprod(axis=1)\n",
    "\n",
    "omega = P0.rvs(size=(N, K))\n",
    "\n",
    "sample_cdfs = (w[..., np.newaxis] * np.less.outer(omega, x_plot)).sum(axis=1)\n",
    "\n",
    "r_ax.plot(x_plot, sample_cdfs[0], c='gray', alpha=0.75,\n",
    "          label='DP sample CDFs');\n",
    "r_ax.plot(x_plot, sample_cdfs[1:].T, c='gray', alpha=0.75);\n",
    "r_ax.plot(x_plot, P0.cdf(x_plot), c='k', label='Base CDF');\n",
    "\n",
    "r_ax.set_title(r'$\\alpha = {}$'.format(alpha));\n",
    "r_ax.legend(loc=2);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dirichlet process mixtures\n",
    "\n",
    "For the task of density estimation, the (almost sure) discreteness of samples from the Dirichlet process is a significant drawback.  This problem can be solved with another level of indirection by using Dirichlet process mixtures for density estimation.  A Dirichlet process mixture uses component densities from a parametric family $\\mathcal{F} = \\{f_{\\theta}\\ |\\ \\theta \\in \\Theta\\}$ and represents the mixture weights as a Dirichlet process.  If $P_0$ is a probability measure on the parameter space $\\Theta$, a Dirichlet process mixture is the hierarchical model\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "    x_i\\ |\\ \\theta_i\n",
    "        & \\sim f_{\\theta_i} \\\\\n",
    "    \\theta_1, \\ldots, \\theta_n\n",
    "        & \\sim P \\\\\n",
    "    P\n",
    "        & \\sim \\textrm{DP}(\\alpha, P_0).\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "To illustrate this model, we simulate draws from a Dirichlet process mixture with $\\alpha = 2$, $\\theta \\sim N(0, 1)$, $x\\ |\\ \\theta \\sim N(\\theta, (0.3)^2)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 5\n",
    "K = 30\n",
    "\n",
    "alpha = 2\n",
    "P0 = sp.stats.norm\n",
    "f = lambda x, theta: sp.stats.norm.pdf(x, theta, 0.3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "beta = sp.stats.beta.rvs(1, alpha, size=(N, K))\n",
    "w = np.empty_like(beta)\n",
    "w[:, 0] = beta[:, 0]\n",
    "w[:, 1:] = beta[:, 1:] * (1 - beta[:, :-1]).cumprod(axis=1)\n",
    "\n",
    "theta = P0.rvs(size=(N, K))\n",
    "\n",
    "dpm_pdf_components = f(x_plot[np.newaxis, np.newaxis, :], theta[..., np.newaxis])\n",
    "dpm_pdfs = (w[..., np.newaxis] * dpm_pdf_components).sum(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "ax.plot(x_plot, dpm_pdfs.T, c='gray');\n",
    "\n",
    "ax.set_yticklabels([]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now focus on a single mixture and decompose it into its individual (weighted) mixture components."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "ix = 1\n",
    "\n",
    "ax.plot(x_plot, dpm_pdfs[ix], c='k', label='Density');\n",
    "ax.plot(x_plot, (w[..., np.newaxis] * dpm_pdf_components)[ix, 0],\n",
    "        '--', c='k', label='Mixture components (weighted)');\n",
    "ax.plot(x_plot, (w[..., np.newaxis] * dpm_pdf_components)[ix].T,\n",
    "        '--', c='k');\n",
    "\n",
    "ax.set_yticklabels([]);\n",
    "ax.legend(loc=1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sampling from these stochastic processes is fun, but these ideas become truly useful when we fit them to data.  The discreteness of samples and the stick-breaking representation of the Dirichlet process lend themselves nicely to Markov chain Monte Carlo simulation of posterior distributions.  We will perform this sampling using `PyMC3`.\n",
    "\n",
    "Our first example uses a Dirichlet process mixture to estimate the density of waiting times between eruptions of the [Old Faithful](https://en.wikipedia.org/wiki/Old_Faithful) geyser in [Yellowstone National Park](https://en.wikipedia.org/wiki/Yellowstone_National_Park)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "old_faithful_df = pd.read_csv(pm.get_data('old_faithful.csv'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For convenience in specifying the prior, we standardize the waiting time between eruptions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "old_faithful_df['std_waiting'] = (old_faithful_df.waiting - old_faithful_df.waiting.mean()) / old_faithful_df.waiting.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>eruptions</th>\n",
       "      <th>waiting</th>\n",
       "      <th>std_waiting</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>3.600</td>\n",
       "      <td>79</td>\n",
       "      <td>0.596025</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>1.800</td>\n",
       "      <td>54</td>\n",
       "      <td>-1.242890</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>3.333</td>\n",
       "      <td>74</td>\n",
       "      <td>0.228242</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>2.283</td>\n",
       "      <td>62</td>\n",
       "      <td>-0.654437</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>4.533</td>\n",
       "      <td>85</td>\n",
       "      <td>1.037364</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   eruptions  waiting  std_waiting\n",
       "0      3.600       79     0.596025\n",
       "1      1.800       54    -1.242890\n",
       "2      3.333       74     0.228242\n",
       "3      2.283       62    -0.654437\n",
       "4      4.533       85     1.037364"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "old_faithful_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "n_bins = 20\n",
    "ax.hist(old_faithful_df.std_waiting, bins=n_bins, color=blue, lw=0, alpha=0.5);\n",
    "\n",
    "ax.set_xlabel('Standardized waiting time between eruptions');\n",
    "ax.set_ylabel('Number of eruptions');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Observant readers will have noted that we have not been continuing the stick-breaking process indefinitely as indicated by its definition, but rather have been truncating this process after a finite number of breaks.  Obviously, when computing with Dirichlet processes, it is necessary to only store a finite number of its point masses and weights in memory.  This restriction is not terribly onerous, since with a finite number of observations, it seems quite likely that the number of mixture components that contribute non-neglible mass to the mixture will grow slower than the number of samples.  This intuition can be formalized to show that the (expected) number of components that contribute non-negligible mass to the mixture approaches $\\alpha \\log N$, where $N$ is the sample size.\n",
    "\n",
    "There are various clever [Gibbs sampling](https://en.wikipedia.org/wiki/Gibbs_sampling) techniques for Dirichlet processes that allow the number of components stored to grow as needed.  [Stochastic memoization](http://danroy.org/papers/RoyManGooTen-ICMLNPB-2008.pdf) is another powerful technique for simulating Dirichlet processes while only storing finitely many components in memory.  In this introductory example, we take the much less sophistocated approach of simply truncating the Dirichlet process components that are stored after a fixed number, $K$, of components.  [Ohlssen, et al.](http://fisher.osu.edu/~schroeder.9/AMIS900/Ohlssen2006.pdf) provide justification for truncation, showing that $K > 5 \\alpha + 2$ is most likely sufficient to capture almost all of the mixture weight ($\\sum_{i = 1}^{K} w_i > 0.99$).  In practice, we can verify the suitability of our truncated approximation to the Dirichlet process by checking the number of components that contribute non-negligible mass to the mixture.  If, in our simulations, all components contribute non-negligible mass to the mixture, we have truncated the Dirichlet process too early.\n",
    "\n",
    "Our (truncated) Dirichlet process mixture model for the standardized waiting times is\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "    \\alpha\n",
    "        & \\sim \\textrm{Gamma}(1, 1) \\\\\n",
    "    \\beta_1, \\ldots, \\beta_K\n",
    "        & \\sim \\textrm{Beta}(1, \\alpha) \\\\\n",
    "    w_i\n",
    "        & = \\beta_i \\prod_{j = i - 1}^i (1 - \\beta_j) \\\\\n",
    "    \\\\\n",
    "    \\lambda_1, \\ldots, \\lambda_K\n",
    "        & \\sim \\textrm{Gamma}(10, 1) \\\\\n",
    "    \\tau_1, \\ldots, \\tau_K\n",
    "        & \\sim \\textrm{Gamma}(10, 1) \\\\\n",
    "    \\mu_i\\ |\\ \\lambda_i, \\tau_i\n",
    "        & \\sim N\\left(0, (\\lambda_i \\tau_i)^{-1}\\right) \\\\\n",
    "    \\\\\n",
    "    x\\ |\\ w_i, \\lambda_i, \\tau_i, \\mu_i\n",
    "        & \\sim \\sum_{i = 1}^K w_i\\ N(\\mu_i, (\\lambda_i \\tau_i)^{-1})\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "Note that instead of fixing a value of $\\alpha$, as in our previous simulations, we specify a prior on $\\alpha$, so that we may learn its posterior distribution from the observations.\n",
    "\n",
    "We now construct this model using `pymc3`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = old_faithful_df.shape[0]\n",
    "\n",
    "K = 30"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def stick_breaking(beta):\n",
    "    portion_remaining = tt.concatenate([[1], tt.extra_ops.cumprod(1 - beta)[:-1]])\n",
    "\n",
    "    return beta * portion_remaining"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "with pm.Model() as model:\n",
    "    alpha = pm.Gamma('alpha', 1., 1.)\n",
    "    beta = pm.Beta('beta', 1., alpha, shape=K)\n",
    "    w = pm.Deterministic('w', stick_breaking(beta))\n",
    "\n",
    "    tau = pm.Gamma('tau', 1., 1., shape=K)\n",
    "    lambda_ = pm.Gamma('lambda_', 10., 1., shape=K)\n",
    "    mu = pm.Normal('mu', 0, tau=lambda_ * tau, shape=K)\n",
    "    obs = pm.NormalMixture('obs', w, mu, tau=lambda_ * tau,\n",
    "                           observed=old_faithful_df.std_waiting.values)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We sample from the model 1,000 times using NUTS initialized with ADVI."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using advi...\n",
      "Average Loss = inf:   5%|▌         | 10891/200000 [00:20<05:49, 541.57it/s]   \n",
      "Convergence achieved at 10900\n",
      "Interrupted at 10,899 [5%]: Average Loss = 489.94\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [mu, lambda_, tau, beta, alpha]\n",
      "Sampling 2 chains: 100%|██████████| 7000/7000 [04:06<00:00, 28.44draws/s]\n",
      "There were 87 divergences after tuning. Increase `target_accept` or reparameterize.\n",
      "There were 31 divergences after tuning. Increase `target_accept` or reparameterize.\n",
      "The gelman-rubin statistic is larger than 1.4 for some parameters. The sampler did not converge.\n",
      "The estimated number of effective samples is smaller than 200 for some parameters.\n"
     ]
    }
   ],
   "source": [
    "with model:\n",
    "    trace = pm.sample(1000,\n",
    "                      tune=2500,\n",
    "                      chains=2,\n",
    "                      init='advi',\n",
    "                      nuts_kwargs={'target_accept': 0.9},\n",
    "                      random_seed=SEED)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The posterior distribution of $\\alpha$ is highly concentrated between 0.25 and 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x144 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.traceplot(trace, var_names=['alpha']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To verify that truncation is not biasing our results, we plot the posterior expected mixture weight of each component."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "plot_w = np.arange(K) + 1\n",
    "\n",
    "ax.bar(plot_w - 0.5, trace['w'].mean(axis=0), width=1., lw=0);\n",
    "\n",
    "ax.set_xlim(0.5, K);\n",
    "ax.set_xlabel('Component');\n",
    "\n",
    "ax.set_ylabel('Posterior expected mixture weight');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that only three mixture components have appreciable posterior expected weights, so we conclude that truncating the Dirichlet process to forty components has not appreciably affected our estimates.\n",
    "\n",
    "We now compute and plot our posterior density estimate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_pdf_contribs = sp.stats.norm.pdf(np.atleast_3d(x_plot),\n",
    "                                      trace['mu'][:, np.newaxis, :],\n",
    "                                      1. / np.sqrt(trace['lambda_'] * trace['tau'])[:, np.newaxis, :])\n",
    "post_pdfs = (trace['w'][:, np.newaxis, :] * post_pdf_contribs).sum(axis=-1)\n",
    "\n",
    "post_pdf_low, post_pdf_high = np.percentile(post_pdfs, [2.5, 97.5], axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "n_bins = 20\n",
    "ax.hist(old_faithful_df.std_waiting.values, bins=n_bins, density=True,\n",
    "        color=blue, lw=0, alpha=0.5);\n",
    "\n",
    "ax.fill_between(x_plot, post_pdf_low, post_pdf_high,\n",
    "                color='gray', alpha=0.45);\n",
    "ax.plot(x_plot, post_pdfs[0],\n",
    "        c='gray', label='Posterior sample densities');\n",
    "ax.plot(x_plot, post_pdfs[::100].T, c='gray');\n",
    "ax.plot(x_plot, post_pdfs.mean(axis=0),\n",
    "        c='k', label='Posterior expected density');\n",
    "\n",
    "ax.set_xlabel('Standardized waiting time between eruptions');\n",
    "\n",
    "ax.set_yticklabels([]);\n",
    "ax.set_ylabel('Density');\n",
    "\n",
    "ax.legend(loc=2);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As above, we can decompose this density estimate into its (weighted) mixture components."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "n_bins = 20\n",
    "ax.hist(old_faithful_df.std_waiting.values, bins=n_bins, density=True,\n",
    "        color=blue, lw=0, alpha=0.5);\n",
    "\n",
    "ax.plot(x_plot, post_pdfs.mean(axis=0),\n",
    "        c='k', label='Posterior expected density');\n",
    "ax.plot(x_plot, (trace['w'][:, np.newaxis, :] * post_pdf_contribs).mean(axis=0)[:, 0],\n",
    "        '--', c='k', label='Posterior expected mixture\\ncomponents\\n(weighted)');\n",
    "ax.plot(x_plot, (trace['w'][:, np.newaxis, :] * post_pdf_contribs).mean(axis=0),\n",
    "        '--', c='k');\n",
    "\n",
    "ax.set_xlabel('Standardized waiting time between eruptions');\n",
    "\n",
    "ax.set_yticklabels([]);\n",
    "ax.set_ylabel('Density');\n",
    "\n",
    "ax.legend(loc=2);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Dirichlet process mixture model is incredibly flexible in terms of the family of parametric component distributions $\\{f_{\\theta}\\ |\\ f_{\\theta} \\in \\Theta\\}$.  We illustrate this flexibility below by using Poisson component distributions to estimate the density of sunspots per year. This dataset can be downloaded from http://www.sidc.be/silso/datafiles. Source: WDC-SILSO, Royal Observatory of Belgium, Brussels."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "sunspot_df = pd.read_csv(pm.get_data('sunspot.csv'), sep=';', names=['time', 'sunspot.year'], usecols=[0, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>time</th>\n",
       "      <th>sunspot.year</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>1700.5</td>\n",
       "      <td>8.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>1701.5</td>\n",
       "      <td>18.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>1702.5</td>\n",
       "      <td>26.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>1703.5</td>\n",
       "      <td>38.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>1704.5</td>\n",
       "      <td>60.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     time  sunspot.year\n",
       "0  1700.5           8.3\n",
       "1  1701.5          18.3\n",
       "2  1702.5          26.7\n",
       "3  1703.5          38.3\n",
       "4  1704.5          60.0"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sunspot_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For this example, the model is\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "    \\alpha\n",
    "        & \\sim \\textrm{Gamma}(1, 1) \\\\\n",
    "    \\beta_1, \\ldots, \\beta_K\n",
    "        & \\sim \\textrm{Beta}(1, \\alpha) \\\\\n",
    "    w_i\n",
    "        & = \\beta_i \\prod_{j = i - 1}^i (1 - \\beta_j) \\\\\n",
    "    \\\\\n",
    "    \\lambda_i, \\ldots, \\lambda_K\n",
    "        & \\sim \\textrm{Gamma}(300, 2)\n",
    "    \\\\\n",
    "    x\\ |\\ w_i, \\lambda_i\n",
    "        & \\sim \\sum_{i = 1}^K w_i\\ \\textrm{Poisson}(\\lambda_i).\n",
    "\\end{align*}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "K = 50\n",
    "N = sunspot_df.shape[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "with pm.Model() as model:\n",
    "    alpha = pm.Gamma('alpha', 1., 1.)\n",
    "    beta = pm.Beta('beta', 1, alpha, shape=K)\n",
    "    w = pm.Deterministic('w', stick_breaking(beta))\n",
    "    # Gamma is conjugate prior to Poisson\n",
    "    lambda_ = pm.Gamma('lambda_', 300.,2., shape=K)\n",
    "    obs = pm.Mixture('obs', w, pm.Poisson.dist(lambda_), observed=sunspot_df['sunspot.year'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using advi...\n",
      "Average Loss = 3,146.3:   9%|▉         | 17979/200000 [00:44<07:33, 401.40it/s]\n",
      "Convergence achieved at 18000\n",
      "Interrupted at 17,999 [8%]: Average Loss = 4,021.5\n",
      "Multiprocess sampling (4 chains in 2 jobs)\n",
      "NUTS: [lambda_, beta, alpha]\n",
      "Sampling 4 chains: 100%|██████████| 28000/28000 [40:43<00:00, 11.46draws/s]  \n",
      "There were 28 divergences after tuning. Increase `target_accept` or reparameterize.\n",
      "There were 17 divergences after tuning. Increase `target_accept` or reparameterize.\n",
      "There were 17 divergences after tuning. Increase `target_accept` or reparameterize.\n",
      "There were 38 divergences after tuning. Increase `target_accept` or reparameterize.\n",
      "The gelman-rubin statistic is larger than 1.4 for some parameters. The sampler did not converge.\n",
      "The estimated number of effective samples is smaller than 200 for some parameters.\n"
     ]
    }
   ],
   "source": [
    "with model:\n",
    "    trace = pm.sample(2000, \n",
    "                      tune=5000,\n",
    "                      chains=4,\n",
    "                      init='advi',\n",
    "                      nuts_kwargs={'target_accept': 0.8},\n",
    "                      random_seed=SEED)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the sunspot model, the posterior distribution of $\\alpha$ is concentrated between 0.6 and 1.2, indicating that we should expect more components to contribute non-negligible amounts to the mixture than for the Old Faithful waiting time model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x144 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.traceplot(trace, var_names=['alpha']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Indeed, we see that between ten and fifteen mixture components have appreciable posterior expected weight."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "plot_w = np.arange(K) + 1\n",
    "\n",
    "ax.bar(plot_w - 0.5, trace['w'].mean(axis=0), width=1., lw=0);\n",
    "\n",
    "ax.set_xlim(0.5, K);\n",
    "ax.set_xlabel('Component');\n",
    "\n",
    "ax.set_ylabel('Posterior expected mixture weight');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now calculate and plot the fitted density estimate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_plot = np.arange(250)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_pmf_contribs = sp.stats.poisson.pmf(np.atleast_3d(x_plot),\n",
    "                                         trace['lambda_'][:, np.newaxis, :])\n",
    "post_pmfs = (trace['w'][:, np.newaxis, :] * post_pmf_contribs).sum(axis=-1)\n",
    "\n",
    "post_pmf_low, post_pmf_high = np.percentile(post_pmfs, [2.5, 97.5], axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "ax.hist(sunspot_df['sunspot.year'].values, bins=40, density=True, lw=0, alpha=0.75);\n",
    "\n",
    "ax.fill_between(x_plot, post_pmf_low, post_pmf_high,\n",
    "                 color='gray', alpha=0.45)\n",
    "ax.plot(x_plot, post_pmfs[0],\n",
    "        c='gray', label='Posterior sample densities');\n",
    "ax.plot(x_plot, post_pmfs[::200].T, c='gray');\n",
    "ax.plot(x_plot, post_pmfs.mean(axis=0),\n",
    "        c='k', label='Posterior expected density');\n",
    "\n",
    "ax.set_xlabel('Yearly sunspot count');\n",
    "ax.set_yticklabels([]);\n",
    "ax.legend(loc=1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, we can decompose the posterior expected density into weighted mixture densities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "ax.hist(sunspot_df['sunspot.year'].values, bins=40, density=True, lw=0, alpha=0.75);\n",
    "ax.plot(x_plot, post_pmfs.mean(axis=0),\n",
    "        c='k', label='Posterior expected density');\n",
    "ax.plot(x_plot, (trace['w'][:, np.newaxis, :] * post_pmf_contribs).mean(axis=0)[:, 0],\n",
    "        '--', c='k', label='Posterior expected\\nmixture components\\n(weighted)');\n",
    "ax.plot(x_plot, (trace['w'][:, np.newaxis, :] * post_pmf_contribs).mean(axis=0),\n",
    "        '--', c='k');\n",
    "\n",
    "ax.set_xlabel('Yearly sunspot count');\n",
    "ax.set_yticklabels([]);\n",
    "ax.legend(loc=1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An earlier version of this example first appeared [here](http://austinrochford.com/posts/2016-02-25-density-estimation-dpm.html)."
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Agenda",
   "title_sidebar": "Agenda",
   "toc_cell": true,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": true
  },
  "widgets": {
   "state": {},
   "version": "1.1.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
